Problem: Chubby Yang is studying linear equations right now. He came up with a nice problem. In the problem you are given an n × n matrix W, consisting of integers, and you should find two n × n matrices A and B, all the following conditions must hold: 

  * Aij = Aji, for all i, j (1 ≤ i, j ≤ n); 
  * Bij = - Bji, for all i, j (1 ≤ i, j ≤ n); 
  * Wij = Aij + Bij, for all i, j (1 ≤ i, j ≤ n). 



Can you solve the problem?

Input

The first line contains an integer n (1 ≤ n ≤ 170). Each of the following n lines contains n integers. The j-th integer in the i-th line is Wij (0 ≤ |Wij| < 1717).

Output

The first n lines must contain matrix A. The next n lines must contain matrix B. Print the matrices in the format equal to format of matrix W in input. It is guaranteed that the answer exists. If there are multiple answers, you are allowed to print any of them.

The answer will be considered correct if the absolute or relative error doesn't exceed 10 - 4.

Examples

Input

2
1 4
3 2


Output

1.00000000 3.50000000
3.50000000 2.00000000
0.00000000 0.50000000
-0.50000000 0.00000000


Input

3
1 2 3
4 5 6
7 8 9


Output

1.00000000 3.00000000 5.00000000
3.00000000 5.00000000 7.00000000
5.00000000 7.00000000 9.00000000
0.00000000 -1.00000000 -2.00000000
1.00000000 0.00000000 -1.00000000
2.00000000 1.00000000 0.00000000

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Scanner;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author hbayramov
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Task solver = new Task();
        solver.solve(1, in, out);
        out.close();
    }

    static class Task {
        public void solve(int testNumber, Scanner in, PrintWriter out) {
            int n = in.nextInt();

            /**
             * Wij = 2Aij
             * Bij = Wij - Aij
             */

            double[][] W = new double[n][n];
            double[][] A = new double[n][n];
            double[][] B = new double[n][n];

            for (int i = 0; i < n; ++i) {
                for (int j = 0; j < n; ++j)
                    W[i][j] = in.nextDouble();
            }

            for (int i = 0; i < n; ++i) {
                for (int j = 0; j <= i; ++j)
                    A[i][j] = A[j][i] = (W[i][j] + W[j][i]) / 2.0d;
            }

            for (int i = 0; i < n; ++i) {
                for (int j = 0; j <= i; ++j) {
                    B[i][j] = W[i][j] - A[i][j];
                    B[j][i] = A[i][j] - W[i][j];
                }
            }

            for (int i = 0; i < n; ++i) {
                for (int j = 0; j < n; ++j)
                    out.printf("%.8f ", A[i][j]);

                out.println();
            }

            for (int i = 0; i < n; ++i) {
                for (int j = 0; j < n; ++j)
                    out.printf("%.8f ", B[i][j]);

                out.println();
            }
        }

    }
}